As the Liberal Party seeks to heal wounds from a failed attempt to install Home Affairs Minister Peter Dutton as prime minister, conservatives within the party are seeking to depose another moderate from within their federal ranks.

Four women have nominated for pre-selection, with former Liberal Party senior vice-president Wendy Summers among the front-runners.

She is the sister of incumbent Tasmanian senator David Bushby, who along with Eric Abetz and Jonathon Duniam received a six-year term.

The Senate pre-selection contest is turning into a personal, bitter battle, with Senator Colbeck and his wife having spent weeks on the campaign trail seeking to get Mr Whiteley elected in last month's Braddon by-election.

Mr Whiteley, who refused to comment when contacted by the ABC, called Senator Colbeck, as a courtesy, to tell him he would be seeking pre-selection.

Senator Colbeck, then the tourism minister, was dropped to fifth on the ballot in 2016, and despite attracting almost 13,500 individual votes — which was the most of any Liberal on the ticket — it was not enough for him to be re-elected.

He did, however, return to the Senate after former senator Stephen Parry lost his seat.

The ABC contacted Senator Abetz, who has been accused as being behind the moves against Senator Colbeck, but he said it was a matter for Tasmania party members.

Senator Abetz lost his frontbech position when Malcolm Turnbull replaced Tony Abbott as prime minister in 2015, a change that led to Senator Colbeck's promotion.

Party members that spoke with the ABC said one of the reasons Senator Colbeck was dropped down the ticket in 2016 was because he had taken the pre-selection for granted, and failed to convince party elders he should get a winnable spot on the ticket.

Following his promotion under Mr Morrison, Senator Colbeck told ABC Radio Hobart that he hoped pre-selectors would put him at the top of the ticket.

"I'm working steadily around the pre-selectors, talking to them, receiving positive feedback but that's a matter for the organisation," he said.

"I'm pitching to lead the ticket as the only sitting senator on this half but also now as a member of ministry.

"I think I've got a few credentials on the table in support of the candidacy and look forward to the support of the panel."

Anne Ruston, Jane Hume have faced similar problems

The conservative moves against Senator Colbeck come after South Australian senator and assistant minister Anne Ruston also faced a similar battle.

Conservative Liberal MPs, some of whom were linked to the effort to have Mr Turnbull removed as prime minister, had attempted to have her dropped down the ticket.

But Senator Ruston held off the challenge and secured the top of the Liberal ticket for the next election.

There is also an effort underway to have Victorian senator Jane Hume dropped down the ticket to a position that would make it difficult for her to regain her seat.

It is not just the Liberal Party facing factional battles that could risks incumbents losing their seats, as Tasmanian Labor senator Lisa Singh is also facing a factional battle.

She was put in a typically unwinnable spot at the last election, but won her seat back in the Senate after more than 20,000 people voted for her below the line.